For the given expressions we will have:
y = exp(x - 4) →we have a shift of 4 units to the right.
y = exp (x +9) → we have a shift of 9 units to the left.
y = exp(x) + 7 → we have a shift of 7 units up.
y = exp(x) - 6 → we have a shift of 6 units down.
<h3>
How to work with vertical and horizontal shifts?</h3>
Remember that the shifts work as follows.
For a function f(x), we define a vertical shift of N units as:
g(x) = f(x) + N
- If N > 0, the shift is upwards.
- If N < 0, the shift is downwards.
For a function f(x), we define a horizontal shift of N units as:
g(x) = f(x + N)
- If N > 0, the shift is to the left.
- If N < 0, the shift is to the right.
Then, if we have:
exp(x - 4) we have a shift of 4 units to the right.
exp (x +9) we have a shift of 9 units to the left.
exp(x) + 7 we have a shift of 7 units up.
exp(x) - 6 we have a shift of 6 units down.
Learn more about translations
brainly.com/question/24850937
#SPJ1
Answer:
21cm
Step by step:
Scale : 9cm :12m
Therefore 1m = 9/12 cm
28m= 9/12 *28 = <u>21 cm</u>
Answer:
4x² - 6x
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Distributive Property
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define</u>
(3x² + 2y² - 3x) + (2x² + y² - 2x) - (x² + 3y² + x)
<u>Step 2: Simplify</u>
- [Distributive Property] Distribute negative: 3x² + 2y² - 3x + 2x² + y² - 2x - x² - 3y² - x
- Combine like terms (x²): 4x² + 2y² - 3x + y² - 2x - 3y² - x
- Combine like terms (y²): 4x² - 3x - 2x - x
- Combine like terms (x): 4x² - 6x
Answer: 3.87132498658 in other words 3.871
Step-by-step explanation:
I don't know the area of a parallelogram off the top of my head but you can use the area of the rectangle and the area of the triangle and add those. The area of the triangle is 1/2*base*height and use the pythagorean theorem to find the base. 3² + b² = 5²; 9 + b² = 25; b² = 16; b = 4. The area of the triangle is 1/2*4*3 or 6 in. Since there are two of them, the total area of the triangles are 12 in. The area of the rectangle is length*width or (12 - 4) * 3 which is 8 * 3 or 24in. Add these areas together to get 36in total
